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How to Calculate Statistical Sample Sizes

By Michael Keenan; Updated April 24, 2017

Sample size is very important to ensure that an experiment yields statistically significant results. If the sample size is too small, the results will not give actionable results because the variation will not be large enough to conclude that the result wasn't due to chance. If a researcher uses too many individuals, the study will be costly and may not get the funding that it needs. Therefore, those conducting surveys need to understand how to estimate the necessary sample size.

Decide the confidence interval needed. This is how close the results of the study should be to the proportion in real life. For example, if a pre-election poll shows 60% of the people support candidate A and the confidence interval is 3%, the true proportion should lie between 57and 63.

Decide the confidence level needed. The confidence level is different from a confidence interval because it represent how certain the researcher can be that the true percentage lies within the confidence interval. The confidence level is written as a Z-score, which is the number of standard deviations away from the mean the range includes. A confidence level of 95 percent includes 1.96 standard deviations on either side of the mean, so the Z-score would be 1.96. This means that there is a 95 percent chance that the actual proportion is within 1.96 standard deviations on either side of the study result.

Estimate the proportion for the study. For example, if 55% of the respondents are expected to support candidate A, use 0.55 for the proportion.

Use the numbers already found to determine the answer with the following formula:

Sample size is equal to the confidence level squared times the proportion times the quantity of 1 minus the proportion divided by the confidence interval squared

SS = (Z^2 * P * (1 - P))/C^2

For example, if you needed to know with 95 percent confidence, expected the proportion to be 65 percent, and needed the study proportion to be plus or minus 3 percentage points, you would use 1.96 as Z, 0.65 as P, and 0.03 as C, which would reveal the need for 972 people in the survey.

Tip

Choose an appropriate confidence level. A study researching discrimination would need a higher confidence level than a study comparing the batting averages of two baseball players.

Warning

Estimate carefully and err on the side of a more balanced (50/50) result. The closer the proportion is to 50/50, the larger the sample size needed.

References

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."